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PRECALCULUS

James B. asked • 01/11/20

Find the inverse of f informally . Verify that f(f ^ (- 1) * (x)) = x and f ^ (- 1) * (f(x)) = x f(x) = sqrt(x)

You are verifying f(x)= square root x

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By:

Kerri P. answered • 01/11/20

TUTOR 5 (375)

Certified Mathematics Teacher Grades 7-12

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We are starting out with f(x) = √x. Note that this function has a domain of x ≥ 0 and range of y ≥ 0.

To find the inverse function, switch the x and y (f(x)) and re-solve for y:

x = √y square both sides

y = x2

f-1(x) = x2, however we need to consider the domain and range

Since the range of f(x) was restricted to y ≥ 0 that means that the domain of f-1(x) is restricted to x ≥ 0 as well.

So technically f-1(x) = x2, for x ≥ 0 (just the right half of the parabola)

Next, you are asked to use composition of functions to verify.

f(f-1(x)) = √(x2) = x when x ≥ 0

f-1(f(x)) = (√x)2 = x when x ≥ 0

Therefore, they are inverses on the restricted domain.