FUNCTION NOTATION WORKSHEET FOR SAT

Problem 1 :

If f(x) = 2x√x, then for which of the following values of x does f(x) = x?

A) 1/4     B) 1/2     C) 2     D) 4      E) 8

Solution

Problem 2 :

If f(a) = a^-3 - a^-2, then f(1/3) =

A) -1/6          B) 1/6      C) 6       D) 9       E) 18

Solution

Problem 3 :

If f(x) = x² + 3x - 4, then f(2 + a) =

A) a² + 7a + 6     B) 2a² - 7a - 12      C) a² + 12a + 3

D) 6a² + 3a + 7       E) a² - a + 6

Solution

Problem 4 :

If f(x) = x² and g(x) = x + 3, then g(f(x)) =

A) x + 3     B) x² + 6     C) x + 9     D) x² + 3      E) x³ + 3x²

Solution

Problem 5 :

If f(x) = x/2, then f(x²) √ (f(x))² =

A) x³/4       B) 1          C) 2x²       D) 2        E) 2x

Solution

Problem 6 :

If f(x) = √x + 1, and if the domain of x is the set {3, 8, 15}, then which of the following sets indicates the range of f(x)?

A) {-4, -3, -2, 2, 3, 4}     B) {2, 3, 4}         C) {4, 9, 16}

D) {3, 8, 15}            E) {all real numbers}

Solution

Problem 7 :

If f(a) = 6a - 4, and if the domain of a consists of all real numbers defined by the inequality -6 < a < 4, then the range of f(a) contains all of the following members EXPECT.

A) -24       B) √1/6      C) 0       D) 4      E) 20

Solution

Problem 8 :

If the range of the function f(x) = x² - 2x - 3 is the set R = {0}, then which of the following sets indicates the largest possible domain of x?

A) {-3}      B) {3}     C) {-1}    D) {3, -1}     E) all real numbers

Solution

Problem 9 :

If f(x) = √x² - 5x + 6, which of the following indicates the set of all values of x at which the function is NOT defined?

A) {x| x < 3}      B) {x| 2 < x < 3}      C) {x| x < -2}

D) {x| -3 < x < 2}        E) {x| x < -3}

Solution

Problem 10 :

If f(x) = ∛1/x, then the largest possible domain of x is the set that includes

A) all non zero integers

B) all non negative real numbers

C) all real numbers except 0      D) all positive real numbers

E) all real numbers

Solution