Question

Let f(x) = StartFraction x squared minus 5 x + 4 Over x minus 1 EndFraction and g(x) = 2 Superscript x minus 3. For which value of x does f(g(x)) have a discontinuity?

Answer 1

9514 1404 393

Answer:

x=1

Explanation:

The function f(x) is undefined where its denominator (x+1) is zero. That will be the case for x=-1.

The composition f(g(x)) will give f(x) an argument of -1 when g(x) = -1. That will be the case when ...

2^x -3 = -1

2^x = 2 . . . . . add 3

x = 1 . . . . . . match exponents

f(g(x)) will have a discontinuity at x = 1.