Question 1

Given $$f(x) = x + x^2$ and g(x) = 2x + 1$, what is (f$$ \circ g)(x)$$?

Accepted Answer

$$4x^2 + 6x + 2$

Question 2

What is the inverse function of $$f(x) = 3x + 4$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{x-4}{3}$$

Question 3

What is the inverse function of $$g(x) = (x+1)^3$?

Accepted Answer

$$g^{-1}(x$$) = \sqrt[3]{x} - 1$$

Question 4

What is the domain and range of $$f(x) = 2^x - 3 as $$shown in the first image?

Accepted Answer

Domain: $$(-\infty, \infty)$$; Range: $$(-3, \infty)$$

Question 5

What is the domain and range of $$g(x) = \log_7$ x as $$shown in the second image?

Accepted Answer

Domain: $$(0, \infty)$$; Range: $$(-\infty, \infty)$$

Question 6

Simplify $$\log_5$ 125.$$

Accepted Answer

$$3$$

Question 7

Simplify $$\log_{100} 10.$$

Accepted Answer

$$\frac{1}{2}$$

Question 8

Express $$\log \$$left(a^3$$ b$$^{1/2}$$ c^2$ \right) as an $$equivalent expression using individual logarithms.

Accepted Answer

$$3 \log a + \frac{1}{2} \log b - 2 \log c$$

Question 9

Express $$\frac{1}{3} \log_a x + 2 \log_a z as a $$single logarithm.

Accepted Answer

$$\log_a \left( z^2$ \sqrt[3]{x} \right)$$

Question 10

Evaluate $$\log 25 to $$four decimal places.

Accepted Answer

$$1.3979$$

Question 11

Evaluate $$\ln 0.4 to $$four decimal places.

Accepted Answer

$$-0.9163$$

Question 12

Evaluate $$e^{4.8} to $$four decimal places.

Accepted Answer

$$121.5104$$

Question 13

Find $$\log_3$ 14$$ using the change-of-base formula. Round to four decimal places.

Accepted Answer

$$2.4022$$

Question 14

Solve $$2^x = \frac{1}{32}$$ and approximate to four decimal places.

Accepted Answer

$$-5$$

Question 15

Solve $$\log_4$ x = \frac{1}{2}$$ and approximate to four decimal places.

Accepted Answer

$$2$$

Question 16

Solve $$\log x = -2$$ and approximate to four decimal places.

Accepted Answer

$$0.01$$

Question 17

The population of Nigeria was about 186 million in 2016, with an exponential growth rate of 2.6% per year. What is the exponential function describing the population?

Accepted Answer

$$P(t) = 186e$$^{0.026t}$$

Question 18

An investment with interest compounded continuously doubled itself in 16 years. What was the interest rate?

Accepted Answer

$$0.043 or$$ $$4.3\%$$ per year

Intermediate Algebra: Exponential and Logarithmic Functions – Graphs and Properties

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