a. The function f is such that f(x) = 2x² - 8x + 5.

i. Show that f(x) = 2(x + 1)² + b, where a and b are to be found.

iii. Hence, or otherwise write down a suitable domain for f so that f^-1 exists.

b. The function g and h are defined respectively by g(x) = x² + 4, x ≥ 0, h(x) = 4x - 25, x ≥ 0,

i. Write down the range of g and of h^-1.

ii. On a copy of the exes below sketch the graph of y = g(x) and y = g^-1(x) showing the coordinates of any points where the curves meet the coordinates axes.

iii. Find the value of x for which gh(x) = 85.

Transcribed Image Text:

y1