If and h(x) = 4 – x, what is the value of ?

Asked by maham237 @ 02/12/2020 in Mathematics viewed by 392 People

If g(x)=x+1/x-2 and h(x) = 4 – x, what is the value of g(h(-3))?

Answered by maham237 @ 02/12/2020

g(h(-3)) = ⁸/₅ = 1.6

Further explanation

if g(x)=x+1/x-2 and h(x) = 4 – x, what is the value of g(h(-3))

In this problem we will find out the value of the function composition. There are two ways to do it.

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

$\boxed{ \ h(x) = 4 - x \ }$

$\boxed{ \ g(h(-3)) = ? \ }$

Option 1

Step-1: compose (g o h)(x) = g(h(x))

Here h(x) as input into g(x). In other words, first we apply h(x), then apply g(x) to that result:

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

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

And we get,

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

Step-2: calculate the value of g(h(-3))

After getting g(h(x)) we proceed by calculating the value g(h(-3)).

$x = -3 \rightarrow g(h(x)) = \frac{5 - x}{2 - x}$

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

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

And we obtain the final result:

$\boxed{\boxed{ \ g(h(-3)) = \frac{8}{5} = 1.6 \ }}$

Option 2

Step-1: count h(-3) initially

$x = -3 \rightarrow h(-3) = 4 - (-3)$

And we get,

$\boxed{ \ h(-3) = 7 \ }$

Step-2: calculate the value of g(h(-3))

Here the value of h(-3), i.e. 7, as input into g(x).

$h(-3) = 7 \rightarrow f(7) = \frac{7 + 1}{7 - 2}$

$f(7) = \frac{8}{5}$

Remember, f(7) as g(h(-3))

And we obtain the final result:

$\boxed{\boxed{ \ g(h(-3)) = \frac{8}{5} = 1.6 \ }}$

Learn more

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Keywords: if g(x) = x+1/x-2 and h(x) = 4 – x, what is the value of g(h(-3)), composition function, input, g(h(x)), value, initially, f(7), h(-3)

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