Let f(æ) = 4x + 4 and g(x) = 5æ? + 2æ. After simplifying, (f + g)(x) =

Q: If f(x)=7e^x−10x^3+8, find f'(x).

A:

Q: If f (x) = (4 - x)>(x2 + 3), what is (a) f (a)? (b) f (a + 1)?

A: Given that, f(x)=4-x>x2+3 Consider f(x)=4-xx2+3 instead of f(x)=4-x>x2+3.

Q: If f'(x)=7x ·x -4 and f(4)= - 5, then what is f(5)?

A: A detailed solution is given below.

Q: If f(x) =Vx- 4x + 19, then what is f(1)?

A: We first find f'(x) using the power rule and chain rule.

Q: If f(x) = x2 - 5x + 4, we can find f(x + 6) by replacing each occurrence of_____ by______ .

A: If f(x) = x2 - 5x + 4, we can find f(x + 6) by replacing each occurrence of_____ by______ .

Q: If f'(x)=7x x-4 and f(4)= - 5, then what is f(5)?

A:

Q: If f(x)=x2+10x+25 is true for x≤−5, find f−1(x).

A: We have to find the inverse function of f(x)

Q: If f(x) = /x – 1, which shows fx)?

A:

Q: For what values of x is Ax) concave down if f "(x) = 3x' – 14x² + &r?

A: Given that, f''x=3x3-14x2+8x For what value of x is fx concave down.

Q: Given that f(x) = x² – 3x - 18 and g(x) = x – 6, find f(æ) + g(x) and express the result in standard…

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Q: If f(x) = x2 + 3x + 2, find  f(x + h) - f(x)/h, h ≠ 0, and simplify.

A: Consider the given function fx=x2+3x+2

Q: If f(x) = x-5 and g(x) = 3x2-1, what is (f° g)(x) ? %3D

A: The given functions are:fx=x-5 and gx=3x2-1To find f∘gx

Q: Given that f (x) = 3x² + 1, find (x+h)-f(x) h

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Q: Let h(x)=−2x2+x+4x2+4x−1, what is h′(−5)?

A:

Q: Given, F(x) = 2x+3/4x+5 for x ne-5/4; f^-1(x)

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Q: If f(x) = x² – 5x + 4, we can find f(x + 6) by replacing each occurrence of _by.

A: Given function is fx=x2-5x+4. We can find fx+6 by replacing each occurrence of x by x+6. In the…

Q: Determine the error term of for the formula: f'(x)  ≈ (1/4h) [f(x+3h) - f(x-h)]

A: In order to find the error term of the given expression, first find the value of f(x+3h) and f(x-h).

Q: If f (x) 5x?, then f'(x) = 10x. True False

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Q: If f'(x) = 5x* – 3x2 + 4 and f(-1) = 2, then find f (x).

A:

Q: If f (x) = x2 - 2x - 1, find f (2), f (-3), and f (a).

A: f(x) = x2-2x-1

Q: 6. If f(x) =-2x + ax? +2 and f(2) = 2a, find a.

A: The given function is fx=-2x3+ax2+2. It is given that f(2)=2a.

Q: f(x) = x^2-7x+9 then f'(x) = ?

A:

Q: If f (2) for f (x): +6 is 8, then what is f (8)?

A:

Q: If f(x)= x – 4 and g(x)= Vx – 2; | f which of the following is equal to (x)?

A: Rational function value

Q: Find f(0), if f(x)=3 – 5x + x2.

A: Given function is, fx=3-5x+x2. The objective is to find the f0. Function is described as the special…

Q: If f (x) = x² – 15 and g(æ) = 2x + 4, what is g[f-1'(10)]?

A: GIVEN h(x)=bx2+20  AND h(5)=120  substituting the value of x=5 in h(x) we have  h(5)=b(25)+20…

Q: If f(x)=5x-1, g(0)=2, g'(0)=4, and h(x)=f(g(x)), then what is h'(0)?

A: Given that h(x)=f(g(x)) Using chain rule we get: h'(x)= f'(g(x))g'(x) We plug x=0 So, h'(0)=…

Q: If (f°g)(x)=2x-1,how might f(x) and g(x) be defined?

A: (f°g)(x)=2x-1 can be written as f(g(x)) So g(x) is the inner or the first function  And f(x) is…

Q: If f(x)=f(x)= x^3+5x^2+6x and g(x) x+2,  what is the simplest version of (f/g)(x)?

A:

Q: If f(x) = x2 + 3x + 2, find [f(x + h) - f(x)]/h, h ≠ 0, and simplify.

A: Consider the given function as fx=x2+3x+2

Q: Given f(x) = 7x + 3 ÷ 8   , then f-1 (x)  will be?

A: consider the function f(x)=7x+38 put f(x)=y y=7x+38 replace x with y and y with x  x=7y+38 solve for…

Q: If f(x)=x^2−14x+49 is true for x≥7, find f^-1(x)

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Q: If f(x) = 3x – 4 and 9(x) = x°, what is the value of f(g(2))?

A:

Q: If f(x) = (2² + 5x + 3)“, then s'(#) - [ f'(x) -

A: To find the derivative of the given function, we need to use chain rule of differentiation and some…

Q: Given that f(x) = x² – 8x and g(æ) = x + 6, calculate

A:

Q: Given f(x) = 4x° + 9x* - 8x - 5, how many sign changes are there in the coefficients of f(- x)?

A:

Q: If f (x) = x2 - 4x + 10, find f (-a), f (a - 4), and f (a + h).

A: Given: fx=x2-4x+10

Q: Let f(x) = 4x + 2 and g(x) = 3x2 + 2x. After simplifying, (fo g)(x)

A:

Q: If f(x) = x2 – 5 and g(x) = V x2 + 25,then (fo g)'(x) is equal to

A:

Q: If f(x)= x³ -3x² +2x -1, then what is f' (-1)

A: f(x) = x3 -3x2 +2x -1

Q: If f(x)=2sin^-1(x^3), then f’(x)=?

A: Solution:

Q: If f(x)=2x+1 and g(x)=x^2+5, what is g(f(2))?

A:

Q: Given f(x) = x³ – 2, what is f(2)? |

A:

Q: If f(x) =2x-3 and g(x)=3x-2, what is f x g ?

A:

Q: If f (x) = |3x - 2| and g(x) = |x| + 2, find f (1), f (-1), g(2), and g(-3).

A: fx=3x-2  &  gx=x+2 Now, f1=31-2=1=1 f-1=3-1-2=-5=5

Q: .If f (x) = 5x - 2, g (x) = 2x - 3 and h (x) = x2, then (fogoh) (-1) =

A:

Q: fG)=4x-3 , SC)=Ê (3of) (x)=

A: Givenf(x) = 4x - 3g(x) = x2(f∘f)(x) = ?(g∘f)(x) = ?

Q: if f(x) = x^2-7x/x-7 and g(x) = x is it true that f=g?

A: Here we have given two functions f(x) and g(x). f(x) = x2 - 7xx-7andg(x) = x  And we have to check…

Q: Let h(x)=−2x^2+x+4/x^2+4x−1, what is h′(−5)?

A:

Transformation of Graphs

The word ‘transformation’ means modification. Transformation of the graph of a function is a process by which we modify or change the original graph and make a new graph.

Exponential Functions

The exponential function is a type of mathematical function which is used in real-world contexts. It helps to find out the exponential decay model or exponential growth model, in mathematical models. In this topic, we will understand descriptive rules, concepts, structures, graphs, interpreter series, work formulas, and examples of functions involving exponents.