Let f1 and f2 be functions from R to R such that f1(x) = x2 and f2(x) = x − x2. What are the functions f1 + f2 and f1 f2?

Q: Evaluate each expression using the functions

A: Given; f(x)=xx-2 Let  f∘gx=x⇒f-1=g We have, f(x)=xx-2 Assume,…

Q: Let f(x) = x³ + 2, g(x) = x- - 3, and h(x) = 8x + 3. Find the rule for the function. %3D f-g

A: Given function is : fx=x3+2gx=x2-3hx=8x+3  To find the value of fx-gxhx

Q: Let f(x) = { 2x-3. 3x²+2, if x < 3 if x ≥ 3 be a piecewise function. Evaluate Sof 0 f(x)dx=

A: We can find the integration of the piecewise function as below.

Q: Find f g and g of, where f (x) = x^2 + 1 and g(x) =3x + 2, are functions from R to R.

A:

Q: Let f(x) = m1x + a and g(x) = m2x + b, where m1, m2, a, and b are constants. Determine the necessary…

A: f∘g=g∘ffgx=gfxfm2x+b=gm1x+am1m2x+b+a=m2m1x+a+bm1m2x+m1b+a=m1m2x+m2a+bm1b-b=m2a-abm1-1=am2-1

Q: Let f(x)=x2+2x. Find all values of c in the interval [−2,0] such that f′(c)=0.

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Q: Express h(x) = (x2 - 3x + 7)9 as a composition of two functions f and g such that h(x) = ( f ∘…

A: To Determine:  Express h(x)  as a composition of two functions f and g such that h(x) = ( f ∘ g)(x).…

Q: Find the domain of the function. h) - 5) X - A) {x|x 0}, or (0, -) B) {x|x 1), or (-, 1) u (1, ) D)…

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Q: 2 For f(x) x 5 and g(x)= 7- x, find b. the domain of f og (fo g)(x); а.

A: Consider the given functions.

Q: Let h(x)=f(x)g(x). If f(x)=x2−3x,g(0)=−1, and g′(0)=−4, what is h′(0)?

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Q: Let f(x)= 4x-1, h(x)= -x+4. Find (fo h)(-2). (foh)(-2) =

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Q: Determine the values of a and b such that the function (x -a ,x 1 Is continuous of all values of x.

A:

Q: Let f(x) = 2x - 1 and g(x) = x2 + x - 2. Find the function: (f - g)(x)

A: fx=2x-1 and gx=x2+x-2

Q: The domain of the function f(x)=√12+4x−x^2 is the closed interval [A,B] where A= and B=

A: Domain is the set of all values that can be taken by x so that the equation is defined.

Q: Let h(x)=f(x)g(x), where f(x)=3x^2−3 and g(x)=x. What is h′(x)?

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Q: Let the function f be defined by 3x - 3, for a 3 Evaluate f(-1) + f(4)

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Q: Let f(æ) = – 3x* In æ %3D f'(x) = f'(e²) =

A:

Q: Let the function f: R → R be defined by 1 x² f(x) = - 0, x = 0, x = 0.

A: Let us solve the given problem on continuity in the next steps.

Q: Let k(x)=f(x)g(x)h(x). If f(x)=−2x−3,g(x)=−3x+3, and h(x)=−3x2+x+1, what is k′(1)?

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Q: Determine the values of x for which f (x)=x",x >0 is increasing or decreasing.

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Q: Prove from the definition of differentiability that the function f : R\{3/2} → R f(x) = 3 – 2x is…

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Q: Let f be a function defined on the real line R and suppose that it satisfies the condition If(x) –…

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Q: Let f(x) 1 + 7x. Determine whether f (x) is even, odd, or neither. = f(-エ) = help (formulas) f(x) =…

A: Given: fx=1x+7x                                            ..1 we know that any given functionfx is…

Q: How many functions f:R→R  exists such that : 2f(x)+2f(y)=f(x+y)+f(x−y)+2y holds for all real x and…

A: By choosing x=y=0. Also by choosing x=y we can see f(2x)=4f(x).  Moreover choose x=0 and use f(0)=0,…

Q: Let h(x)=f(x)g(x). If f(x)=−2x^2+2x+3 and g(x)=−x^2−3x−4, what is h′(−1)?

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Q: Find the differnce quotient f(x)=f(x+h)-f(x)/h of the function f(x)= 4x^2-5 DQ= 2x+h DQ= 8x+h DQ=…

A: on using given formula we get last option is true

Q: Let h(x)=f(x)/g(x), where f(x)=−2x−3 and g(x)=x^2−x+2. What is h′(x)?

A: Use quotient rule to derivative

Q: Let h(x)=f(x)g(x). If f(x)=4x^2+3x+1 and g(x)=3x^2−3x−4, what is h′(−1)?

A: Given: hx=fxgx, fx=4x2+3x+1, gx=3x2-3x-4

Q: Find a function f(x) such that f'(x) = 6x² – 3 and f(0) = 1 - %3D f(x) =|

A: Given:     f'(x) = 6x2 - 3    f(0) = 1

Q: Find the function f(x) such that f' (x) = x²e# with f(0) = 0. O (x² - 2x - 2)e* + 2 O (x2 + x + 2)e*…

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Q: The domain of the function f (x, y) = In(2 – /x² + y² ) is:

A:

Q: Use the intermediate value theorem to show that f has a zero between a and b.

A: We have to use the intermediate value theorem to show that the given function : f(x)=x5+x3+x2+x+1 ,…

Q: Find a function f: Q → Q that is both surjective and injective but not the identity function.

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Q: Let f(x) = √20- x and g(x) = x² - x. Then the domain of fo g is equal to

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Q: 39. Let f(x) = 2x3 - 4. Find a function y = g(x) so that (f o g)(x) =x+2.

A: We use the definition of composition of functions to find y= g(x).

Q: Let h(x) = f(x)g(x). If f(x) = x² + 4x – 1, 9(-2) = 3, and g'(-2) = -5, what is h' (-2)?

A: Given h(x) = f(x)g(x). ƒ(x) = x² + 4x − 1, g(−2) = 3, and g'(-2) = −5,

Q: Show that the function f : R → R given by f(x) = x3 is injective.

A: To show the given function is injective(one-one), first calculate the value of function at two…

Q: Let h(x)=f(x)g(x). If f(x)=3x^2−x−4 and g(x)=−x^2+2, what is h′(−1)?

A:

Q: Let f(x)= {x^2-8x+16, if x≤3/ax+b if x>3 Find a and b such that the function f(x) is differentiable…

A: Given fx=x2-8x+16x≤3ax+bx&gt;3 is differentiable everywhere so it is also continuous.

Q: Let f(x) = Vx - 1 g(x) = v2- x obtaind )(x), and the domain of (x),

A:

Q: Find F as a function of x and evaluate it at x = 2, x = 5, and x = 8.

A: Consider the given: Fx=∫1x20v2dv Find the…

Q: Find (f-1)' (a)   f(x)  = x3 + 3Sin x  + 2Cos x  , a= 2

A: Given expression: fx=x3+3sinx+2cosx Differentiate the above expression w.r.t 'x'…

Q: Find the function f(x) = ax + bx + cx +d for which f( - 3) = - 103, f( - 1) = - 3, f(1) = 1, and…

A: We will use matrix method to solve the equations obtained by given conditions

Q: Express f(x) in the form f(x)=(x-k)q(x)+r for the given value of k. f(x)= 5x^3+x^2+x-2, k=-1

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Q: Find f such that f'(x) = x - 5 and f(0) = 3. f(x) = %3D

A: Given: f'x=x2-5 f0=3   Integrate the function with respect to x. ∫f'x=∫x2-5dxfx=∫x2dx-5∫1dx=x33-5x+C

Q: Express the function H(x) = |7/x - 2 in the form fo g. g(x) = %3D f(x) =

A: H(x) = [7x -2] so here find f*g(x) form here g(x) = 7x -2 and f(x) = [x]

Q: Let the function f: R→ R be defined by { f(x) = 0, 1 x2, x=0, x = 0.

A:

Q: If f is a function of only r, g is a function of only y, and f and g satisfy In(f(x)) + In(g(y)) =…

A: Given: f is a function of the only x and g is a function of the only y.…