Question

It is known that function f is an increasing function that satisfies f(1)=-3 and f'(1)=3. Use this information to compute f⁻¹ (-3).

A. 1
B. -3
C. - 1/3
D. 1/3

Answer 1

To compute f⁻¹ (-3), we need to find the value of x such that f(x) = -3. Since f(1) = -3 and f'(1) = 3, we can conclude that f⁻¹ (-3) is 1/3.

Step-by-step explanation:

To compute f⁻¹ (-3), we need to find the value of x such that f(x) = -3. Since f(1) = -3, we know that the function passes through the point (1, -3). We also know that f'(1) = 3, which means the slope of the function at x = 1 is positive.

Since the function is increasing and passes through the point (1, -3), we can conclude that f(x) must be greater than -3 for x greater than 1. Therefore, f⁻¹ (-3) is less than 1.

From the given options, the only answer choice that is less than 1 is D. 1/3. So the correct answer is D. 1/3.