Question

3. Functions f, g, and h are defined as follows: f(x) = x + 1, g(x) = x2 +1, and h(x) = x + 1. (a) Find the inverse of function g(x). (b) Find f(h(-2)). (c) Find g(f(3)).​

Answer 1

9514 1404 393

Answer:

(a) g^-1(x) = ±√(x -1)

(b) 0

(c) 17

Explanation:

(a) The inverse is found by solving for y:

x = g(y)

x = y² +1

x -1 = y² . . . . . . subtract 1

y = ±√(x-1) . . . . take the square root

g^-1(x) = ±√(x -1) . . . . in functional form

Note: the inverse of g(x) is not a function, because it is double-valued.

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(b) f(h(-2)) = f(-2+1) = f(-1) = f(-1+1)

f(h(-2)) = 0

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(c) g(f(3)) = g(3+1) = g(4) = 4² +1

g(f(3)) = 17