Composite functions
Let ƒ(x) = x³, g (x) = sin x and h(x) = √x.
Find the domain of ƒ o g.

Composite functions

Let ƒ(x) = x³, g (x) = sin x and h(x) = √x .

Evaluate h(g( π/2)).

Composite functions

Let ƒ(x) = x³, g (x) = sin x and h(x) = √x .

Find h (ƒ (x)).

Composite functions

Let ƒ(x) = x³, g (x) = sin x and h(x) = √x.

Find ƒ(g(h( x))).

Composite functions

Let ƒ(x) = x³, g (x) = sin x and h(x) = √x.

Find the domain of g o ƒ.

Composite functions

Let ƒ(x) = x³, g (x) = sin x and h(x) = √x .

Find the domain of ƒ o g.

{Use of Tech} Polynomial calculations

Find a polynomial ƒ that satisfies the following properties. (Hint: Determine the degree of ƒ; then substitute a polynomial of that degree and solve for its coefficients.)

ƒ(ƒ(x)) = 9x - 8

{Use of Tech} Polynomial calculations

Find a polynomial ƒ that satisfies the following properties. (Hint: Determine the degree of ƒ; then substitute a polynomial of that degree and solve for its coefficients.)

ƒ(ƒ(x)) = x⁴ - 12x² + 30

Evaluate and simplify the difference quotients (f(x + h) - f(x)) / h and (f(x) - f(a)) / (x - a) for each function.

f(x) = x² - 2x