Question

What is the value of (g*h)(-3)?

Answer 1

ANSWER


$\boxed {(g \circ \: h)( - 3) = \frac{ 8}{ 5}}$



EXPLANATION

The given functions are:


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


and

$h(x) = 4 - x$


Let us find

$(g \circ \: h)(x)$


This implies that,


$(g \circ \: h)(x) = g(h(x))$


$(g \circ \: h)(x) = g(4 - x)$


$(g \circ \: h)(x) = \frac{4 - x + 1}{4 - x - 2}$


$(g \circ \: h)(x) = \frac{5- x}{2 - x }$



We now substitute x=-3


$(g \circ \: h)( - 3) = \frac{ 5 - - 3}{ 2 - - 3}$



$(g \circ \: h)( - 3) = \frac{ 8}{ 5}$


The correct answer is A

Answer 2

Answer:

The correct answer is choice A.

Step-by-step explanation:

We have given two function.

g(x) = x+1 / x-2

h(x) = 4-x

We have to find the composition of given two functions.

(g*h)(x) = ? and then (g*h)(-3) = ?

(g*h)(x) = g(h(x)

putting the given values of given functions,we have

(g*h)(x) = g(4-x)

(g*h)(x) = 4-x+1 / 4-x-2

(g*h)(x) = 5-x / 2-x

(g*h)(-3) =5-(-3) / 2- (-3)

(g*h)(-3) =5+3 / 2+3

(g*h)(-3) = 8 / 5 Which is the answer.