Question

Jenny works in a picture framing shop. She has a function f(x) equals X +2 that find the size of a square frame, given a picture of side length X in inches. She has a function p(x) equals 3X that gives the price in dollars for the frame. What is the single function that Jenny can use to give a customer a price for a picture with an edge length of X

Answer 1

Given:

The function for size of a square frame is

$f(x)=x+2$

where, x is the side length of the picture.

The function for the price in dollars for the frame is

$p(x)=3x$

To find:

The single function for the price of a picture with an edge length of x.

Solution:

We know that, for a picture with an edge length of x.

Size of a square frame = f(x)

Price in dollars for the frame = p(x)

Single function for the price of a picture with an edge length of x is

$(p\circ f)(x)=p(f(x))$

$(p\circ f)(x)=p(x+2)$       $[\because f(x)=x+2]$

$(p\circ f)(x)=3(x+2)$           $[\because p(x)=3x]$

Let the name of this function is c(x). So,

$c(x)=3(x+2)$

Therefore, the required function is $c(x)=3(x+2)$.