Function Operations, Composition and Inverses: Algebra 2 Math Test – PDF Download

Algebra 2 Inverse Functions Test: questions 1–5

Question 1: Operations on functions (2 points)

Let \(f(x)=x^{2}-3x\) and \(g(x)=2x+5\).

1. \((f+g)(x)\) in simplest form (1 point)
2. \((fg)(2)\) (1 point)

Question 2: Evaluate compositions (2 points)

Let \(f(x)=3x+1\) and \(g(x)=x^{2}-2\).

1. \(f(g(3))\) (1 point)
2. \(g(f(-1))\), using the machine below (1 point)

Question 3: Composite and its domain (2 points)

Let \(f(x)=\frac{2}{x}\) and \(g(x)=x-3\).

1. Write \(f(g(x))\). (1 point)
2. State the domain of \(f(g(x))\). (1 point)

Question 4: Find an inverse (2 points)

Find the inverse function of \(f(x)=\frac{5x-1}{2}\).

Question 5: Verify inverse functions (2 points)

Show that \(f(x)=\frac{x}{3}+4\) and \(g(x)=3x-12\) are inverse functions.

Algebra 2 Inverse Functions Test: questions 6–9

Question 6: Inverse from a graph (2 points)

The graph of the linear function \(f\) is shown with three points.

1. Give the coordinates of the corresponding points on the graph of \(f^{-1}\). (1 point)
2. Write a formula for \(f^{-1}(x)\). (1 point)

Question 7: Restrict the domain (3 points)

The graph of \(f(x)=(x+1)^{2}-4\) is shown.

1. Explain why \(f\) has no inverse function on all real numbers. (1 point)
2. Restrict the domain so that \(f\) has an inverse and find \(f^{-1}(x)\). (1 point)
3. State the domain and range of \(f^{-1}\). (1 point)

Question 8: Taxi fare inverse (3 points)

A taxi fare is \(F(m)=2.50+1.75m\) dollars for a ride of \(m\) miles.

1. Find the inverse function. (1 point)
2. Use it to find how many miles Liam rode when his fare was $20. (1 point)
3. Explain what the inverse function represents. (1 point)

Question 9: Growing circle (2 points)

The radius of a circular ripple is \(r(t)=4t\) inches after \(t\) seconds, and its area is \(A(r)=\pi r^{2}\).

1. Write \(A(r(t))\) in simplest form. (1 point)
2. Find the area after 3 seconds in terms of \(\pi\). (1 point)

How to use this algebra 2 inverse functions test

Take this algebra 2 inverse functions test without notes, then grade it with the test answer key out of 20 points.

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