Question

if f(x)=3x²-1 and g(x)=-2x+7 then(f+g)(-3)

Answer 1

Step-by-step explanation:

A/Q

(f+g)(-3) = (3x²-1-2x+7) (-3)

= 3x²-2x+6-3

= 3x²-2x+3

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Answer 2

Concept

A function is an association between inputs in which each input has a unique link to one or more outputs. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input.

For any two functions $f(x)$ and $g(x)$,

$\[\left( fog \right)(x)=f\left( g(x) \right)\]$

Given

The two functions are $f(x)=3x^{2} -1$ and $g(x)=-2x+7$.

Find

We have to find the value of $(f+g)(-3)$.

Solution

Consider the two functions $f(x)=3x^{2} -1$ and $g(x)=-2x+7$.

Now calculate $f(x)+g(x)$ by adding the two given functions, we get

$f(x)+g(x)=(3x^{2} -1)+(-2x+7)\\f(x)+g(x)=3x^{2} -2x-1+7\\f(x)+g(x)=3x^{2} -2x+6$

This can be written as-

$(f+g)(x)=3x^{2} -2x+6$

Now, to calculate $(f+g)(-3)$, substitute $x=-3$, we get

$(f+g)(-3)=3(-3)^{2} -2(-3)+6$

$(f+g)(-3)=3\times9 +6+6\\(f+g)(-3)=27 +12\\(f+g)(-3)=39$

Hence, $39$ is the required value of $(f+g)(-3)$.

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