Question

FUNCTIONS: In the space provided, type the answer in descending order as it applies without any spaces between the letters, numbers, or symbols.

Type the composition (fog)(x) of the given functions:
f(x) = x^2 + 2x − 6 and g(x) = x + 5.

Answer 1

Hence The composition
`(fog)(x)` of the given function is
`x^2+12x+29`.

Explanation:

Given:

`f(x) = x^2+2x-6`

`g(x)=x+5`

We need to find
`(f o g)(x)`.

Solution:

Now we can say that;

`(f o g)(x)` =
`f(g(x))`

`(fog)(x) = (x+5)^2+2(x+5)-6`

Now Applying distributive property we get;

`(fog)(x) = (x+5)^2+2* x+2*5-6\\\\(fog)(x) = (x+5)^2+2x+10-6\\\\(fog)(x) = (x+5)^2+2x+4`

Now Solving the exponent function we get;

`(fog)(x) = x^2+2* x* 5+5^2+2x+4\\\\(fog)(x) = x^2+10x+25+2x+4\\\\(fog)(x) = x^2+12x+29`

Hence The composition
`(fog)(x)` of the given function is
`x^2+12x+29`.