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

Answer:

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

Step-by-step 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;

$(fog)(x) = (x+5)^2+2\times x+2\times5-6\\\\(fog)(x) = (x+5)^2+2x+10-6\\\\(fog)(x) = (x+5)^2+2x+4$

Now Solving the exponent function we get;

$(fog)(x) = x^2+2\times x\times 5+5^2+2x+4\\\\(fog)(x) = x^2+10x+25+2x+4\\\\(fog)(x) = x^2+12x+29$

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