HW 1.8A

Front

If f(x) = x^2 and g(x) = 3x - 1, find f(g(x)).

Back

f(g(x)) = f(3x - 1) = (3x - 1)^2 = 9x^2 - 6x + 1.

Front

Given f(x) = 3x + 10 and g(x) = x - 2, find f(g(5)).

Back

g(5) = 5 - 2 = 3; f(g(5)) = f(3) = 3(3) + 10 = 19.

Front

Given f(x) = x^2 + 25 and g(x) = x - 5, find (f + g)(x).

Back

(f + g)(x) = f(x) + g(x) = (x^2 + 25) + (x - 5) = x^2 + x + 20.

Front

Given f(x) = 3x^2 + 7x and g(x) = 2x^2 - x - 1, find (f - g)(x).

Back

(f - g)(x) = f(x) - g(x) = (3x^2 + 7x) - (2x^2 - x - 1) = x^2 + 8x + 1.

Front

Which expression represents g(f(x)) if f(x) = 2x - 8 and g(x) = 4x?

Back

g(f(x)) = g(2x - 8) = 4(2x - 8) = 8x - 32.

Front

Definition of function composition.

Back

Function composition is the process of applying one function to the results of another function, denoted as (f ∘ g)(x) = f(g(x)).

Front

What is the formula for the sum of two functions?

Back

The sum of two functions f and g is given by (f + g)(x) = f(x) + g(x).

Front

What is the formula for the difference of two functions?

Back

The difference of two functions f and g is given by (f - g)(x) = f(x) - g(x).

Front

What is the formula for the product of two functions?

Back

The product of two functions f and g is given by (f * g)(x) = f(x) * g(x).

Front

What is the formula for the quotient of two functions?

Back

The quotient of two functions f and g is given by (f / g)(x) = f(x) / g(x), provided g(x) ≠ 0.