Question

If f(x) = 2x - 25 and g(x) = (x + 1) ^ 2 . For what value(s) of x is fg(x) = g(x) ?

Answer 1

x = - 6 , x = 4

Explanation:

firstly find f(g(x)) by substituting x = g(x) into f(x)

f(g(x))

= f((x + 1)²)

= 2(x + 1)² - 25

then equating f(g(x)) = g(x)

2(x + 1)² - 25 = (x + 1)² ← subtract (x + 1)² from both sides

(x + 1)² - 25 = 0 ( add 25 to both sides )

(x + 1)² = 25 ( take square root of both sides )

x + 1 = ±
`√(25)` = ± 5 ( subtract 1 from both sides )

x = - 1 ± 5

then

x = - 1 - 5 = - 6

x = - 1 + 5 = 4