Functions: domain, range, composite and inverse

Question 1 of 10

Given f(x) = 2x − 3 and g(x) = x² + 1, find (a) f(g(x)), (b) g(f(x)), (c) f⁻¹(x), (d) the value of x for which f(g(x)) = g(f(x)).

Question 2 of 10

If f(x) = 4x + 4, find f(1).

Question 3 of 10

Explain the horizontal line test and use it to show that f(x) = x² has no inverse over the real numbers.

Question 4 of 10

The set of all possible inputs of a function is its

Question 5 of 10

Find the inverse of f(x) = 5x + 2.

Question 6 of 10

If f(x) = 5x + 3 and g(x) = 4x − 5, find f(g(3)).

Question 7 of 10

If f(x) = 5x − 1, then f(4) = ___

Question 8 of 10

The inverse of f(x) = x + 3 is x − 3.

Question 9 of 10

The set of all outputs is the

Question 10 of 10

A function f is defined by f(x) = 3x + k and f(2) = 11. Find k and f⁻¹(x).