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In Exercises 35—42, show that f and g are inverses of each other by verifying that
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Precalculus
- Verify that f and g are inverses of each other by showing that f(g(x)) = xand g(f(x)) = x. Give any value(s) of x that need to be excluded from thedomain of f and the domain of g. f(x) = (x − 2)2 for x ≥ 2g(x) = (√x) + 2arrow_forwardShow that f is strictly monotonic on the given interval and therefore has an inverse function on that interval. f(x) = ∣x + 2∣, [−2, ∞)arrow_forwardLet 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)?arrow_forward
- The function f : R → R defined by the formula f(x) = 3x − 5 for all x ∈ R was shown to be one-to-one in Example 2 and onto in Example 4. Find its inversefunction.arrow_forwardShow that f is strictly monotonic on the given interval and therefore has an inverse function on that interval. f(x) = (x − 4)2, [4, ∞)arrow_forwardfind the inverse of the function a) f(x)=cubed square root of x f^-1(x)= , on domain (negative infinity, infinity) b) f(x)=5x+1/2-5x f^-1(x)=arrow_forward
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