Question

Given f(x) = x2 – 7x + 10 and g(x) = x2 – x – 20, find the y-intercept of open parentheses g over f close parentheses of x

0
–2
2 over 3
negative one half

Answer 1

If f(x) is x²-7x+10 and g(x) is x²-x-20, then the y-intercept of (g/f)(x) is 2

Given the functions

• f(x) = x²– 7x + 10

• g(x) = x² – x – 20

First, we need to get the composite function g/f((x)

(g/f)(x) = $\frac{x^2-x-20}{x^2-7x+10}$

The y - intercept of the function occurs at when x = 0

Substitute x = 0 into the resulting expression:

$(g/f)(0)=\frac{x^2-x-20}{x^2-7x-10}\\ (g/f)(0)=\frac{0^2-0-20}{0^2-7(0)-10}\\(g/f)(0)=\frac{-20}{-10}\\(g/f)(0) = 2$

Hence the y-intercept of (g/f)(x) is 2

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