Question

Verify if f(x)=1/2x-2 (and g(x) )= 2x + 4 are inverses.

Answer 1

To find an inverse you switch x and y for a function and solve for y. I will do fx.
X=1/2f(x)'-2
X+2=1/2f(x)'
2x+4=f(x)'
I used ' to represent inverse and since f(x)' =g(x) it is verified

Answer 2

Relations whose inverses are functions are regarded as functions.

f(x) and g(x) are inverses.

The functions are given as:

$\mathbf{f(x) = \frac{1}{2}x - 2}$

$\mathbf{g(x) = 2x + 4}$

If f(x) and g(x) are inverse functions, then:

$\mathbf{f(g(x)) = x}$

We have:

$\mathbf{f(x) = \frac{1}{2}x - 2}$

Substitute g(x) for x

$\mathbf{f(g(x)) = \frac{1}{2}g(x) - 2}$

Substitute $\mathbf{g(x) = 2x + 4}$

$\mathbf{f(g(x)) = \frac{1}{2}(2x + 4) - 2}$

Simplify

$\mathbf{f(g(x)) = x + 2- 2}$

$\mathbf{f(g(x)) = x}$

The above equation is true for inverse functions.

Hence, f(x) and g(x) are inverses.

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