3rd Mid Six Weeks Exam: Inverses and Operations of Functions

Front

Is the inverse of a function also a function?

Back

Yes, the inverse of a function is also a function if it passes the horizontal line test.

Front

What is the result of (f + g)(x) if f(x) = 5x^2 and g(x) = 3x?

Back

(f + g)(x) = 5x^2 + 3x.

Tags

CCSS.HSF-BF.A.1B

Front

How can you determine if two functions are inverses of each other?

Back

Two functions are inverses if (f(g(x)) = x) and (g(f(x)) = x) for all x in the domain.

Tags

CCSS.HSF-BF.B.4B

Front

Evaluate (g∘f)(3) if f(x) = -2x + 2 and g(x) = 2x^2 + 9.

Back

(g∘f)(3) = 41.

Tags

CCSS.HSF-BF.A.1C

Front

What is the result of (f - g)(x) if f(x) = 5x^2 and g(x) = 3x?

Back

(f - g)(x) = 5x^2 - 3x.

Tags

CCSS.HSF-BF.A.1B

Front

What does it mean for a function to be one-to-one?

Back

A function is one-to-one if it never assigns the same value to two different domain elements.

Front

What is the horizontal line test?

Back

The horizontal line test determines if a function is one-to-one by checking if any horizontal line intersects the graph more than once.

Front

If f(x) = 2x + 3, what is f^{-1}(x)?

Back

f^{-1}(x) = (x - 3)/2.

Tags

CCSS.HSF-BF.B.4A

Front

What is the composition of functions?

Back

The composition of functions f and g, denoted (f∘g)(x), is defined as f(g(x)).

Tags

CCSS.HSF-BF.A.1C

Front

What is the domain of the function g(x) = 2x^2 + 9?

Back

The domain of g(x) is all real numbers, (-∞, ∞).