Question

For the function g(x) = 14/x + 3, find (g–1∘ g)(4). a. 6 b. 10 c. 4 d. 0

Answer 1

Answer:

c. 4

Step-by-step explanation:

Given : $g(x)=\frac{14}{x} +3$

First find inverse of g(x)

let g(x)= y

So, $y=\frac{14}{x} +3$

Now replace y by x and x by y

$x=\frac{14}{y} +3$

Now $y = \frac{14}{x-3}$

Thus $g^{-1}(x)=\frac{14}{x-3}$

Now $(g^{-1} \text {o g})(4)$

$(g^{-1} [g(x)])$

$(g^{-1} [\frac{14}{x} +3])$

Now x = 4

$(g^{-1} [\frac{14}{4} +3])$

$g^{-1} 6.5$

Since $g^{-1}(x)=\frac{14}{x-3}$

Put x = 6.5

Since $g^{-1}(6.5)=\frac{14}{6.5-3}$

$g^{-1}(6.5)=\frac{14}{3.5}$

$g^{-1}(6.5)=4$

Thus,  $(g^{-1} \text {o g})(4)=4$

Hence Option C is correct

Answer 2

The function composed with its inverse (g⁻¹) result in x
basically
(g⁻¹o g)(x)=x

so

(g⁻¹o g)(4)=4