Let f(x)=x^2+2 and h(x)=x+6. Find the following value.(f * h)(5)

Question

Let f(x)=x^2+2 and h(x)=x+6. Find the following value.(f * h)(5)

Answer 1

(f * h)(5) =

 

f(5)*h(5)

 

 

Substitute x=5 in the respective functions.

 

(5² + 2)(5 + 6) =

 

(25 + 2)(11) =

 

27(11) =

 

297

Answer 2

If you are given a function F(x) and asked to solve for F(2) then you just plug 2 into the function everywhere there is an x. 

 

When you are given two functions, in this case f(x) and h(x), the same principle applies. It asks you to solve for (f*h)(5) for the given equations. 

 

When you see f(x) you read it as f of x. The parenthesis indicate what you are substituting for x.

 

In this case we have (f*h)(5). So since it is written with f*h together and then the (5). It tells us to first multiply f and h and then substitute 5 for x.

 

f(x) = x² +2

h(x) = x + 6

 

we are going to ignore the 5 for now.

 

so (f*h) = (x²+2)(x+6) 

 

= x³ + 6x² + 2x + 12

 

now we can substitute the 5 for x.

 

(f*h)(5) = (5)³ + 6(5²) + 2(5) + 12

= 297