Composition of Functions

Front

What is the composition of functions?

Back

The composition of functions is a process where one function is applied to the result of another function, denoted as (f ° g)(x) = f(g(x)).

Front

If f(x) = 2x + 3 and g(x) = x - 1, what is g(f(2))?

Back

g(f(2)) = g(2*2 + 3) = g(7) = 7 - 1 = 6.

Front

What does it mean to evaluate a function?

Back

To evaluate a function means to find the output value of the function for a given input value.

Front

If f(x) = x^2 and g(x) = 3x, what is (f ° g)(x)?

Back

(f ° g)(x) = f(g(x)) = f(3x) = (3x)^2 = 9x^2.

Front

What is the formula for finding g(h(x)) if g(x) = 3x + 4 and h(x) = 3x - 1?

Back

g(h(x)) = g(3x - 1) = 3(3x - 1) + 4 = 9x - 3 + 4 = 9x + 1.

Front

How do you find f(-1) if f(x) = 2x^2 + 5x - 17?

Back

f(-1) = 2(-1)^2 + 5(-1) - 17 = 2 - 5 - 17 = -20.

Front

What is the result of (f ° g)(x) if f(x) = x - 5 and g(x) = 3x^2 - 1?

Back

(f ° g)(x) = f(g(x)) = f(3x^2 - 1) = (3x^2 - 1) - 5 = 3x^2 - 6.

Front

Evaluate f(x) = -2x + 13 for f(10).

Back

f(10) = -2(10) + 13 = -20 + 13 = -7.

Front

What is the difference between f(g(x)) and g(f(x))?

Back

f(g(x)) applies g first and then f, while g(f(x)) applies f first and then g, leading to potentially different results.

Front

If f(x) = 3x + 10 and g(x) = x - 2, what is g(f(x))?

Back

g(f(x)) = g(3x + 10) = (3x + 10) - 2 = 3x + 8.