Question

2. Let f(x) = 4x + 12 and g(x) = 4x2 – 12.

(a) What is the inverse of function f?

(b) Is f an inverse of g? Show your work algebraically and explain your answer

Answer:​

Answer 1

(a) f^-1(x) = 1/4x -3

(b) f is not the inverse of g

Explanation:

(a)

The inverse of function f can be found by solving ...

x = f(y)

x = 4y +12

x -12 = 4y

x/4 -3 = y

The inverse of function f is ...

f^-1(x) = 1/4x -3

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(b)

g(x) ≠ f^-1(x), so g^-1(x) ≠ f(x). Function f is not an inverse of g.

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Additional comment

Function g is a quadratic, so it doesn't have an inverse function, except on a restricted domain.

Because g is 2nd degree, any inverse relation will involve a 1/2 power (square root). Both f and its inverse are linear functions, so cannot be inverses of g.