Which of the following functions is one-to-one? A. f ( x ) = 5 x 2 − x B. f ( x ) = 2 x 3 − 3 x 2 C. f ( x ) = 4 x 3 + 3 x D. f ( x ) = √ x − x 4 E. f ( x ) = ln ( x 2 + 1 )

step-by-step explanation:

a and d

part a: 1.08

part b: 27.59

let f (x ) is a function and c be a positive real number,   the graph of the function g (x ) = f (cx ) is represented as follows.

when, c > 1,   the function compresses it in the x - direction.

when, 0 < c < 1, the function stretches it.

the function is g ( x ) = (9x )2.

the heighest power of x in g ( x ) = (9x )2 is 2, so the parent function is square function.

the equation of parent function is f ( x ) = x 2 .

the function is g ( x ) = (9x )2 and the parent function is f ( x ) = x 2 .

so, the functions f and g have the following relationship.

g ( x ) = f ( 9x ).

compare the function g ( x ) = f ( 9x ) with g (x ) = f (cx ).

c = 9 ( > 1 ).

so, the function g (x ) = (9x )2 compresses it in the x - direction.

step-by-step explanation: