MATH SOLVE

3 months ago

Q:
# 100 POINTS BRAINLIEST MATH PROBLEMS

Accepted Solution

A:

Since (f/g)(x) = f(x)/g(x) for x to be in the domain of (f/g)(x) it must be in the domain of f and in the domain of g. You also need to insure that g(x) is not zero since f(x) is divided by g(x). Thus there are 3 conditions. x must be in the domain of f: f(x) = 3x -5 and all real numbers x are in the domain of x.

Given f(x) = 2x + 3 and g(x) = βx2 + 5, find ( f o f )(x).

( f o f )(x) = f ( f (x))

= f (2x + 3)

= 2( ) + 3 ... setting up to insert the input

= 2(2x + 3) + 3

= 4x + 6 + 3

= 4x + 9

Given f(x) = 2x + 3 and g(x) = βx2 + 5, find (g o g)(x).

(g o g)(x) = g(g(x))

= β( )2 + 5 ... setting up to insert the input

= β(βx2 + 5)2 + 5

= β(x4 β 10x2 + 25) + 5

= βx4 + 10x2 β 25 + 5

= βx4 + 10x2 β 20

Given f(x) = 2x + 3 and g(x) = βx2 + 5, find ( f o f )(x).

( f o f )(x) = f ( f (x))

= f (2x + 3)

= 2( ) + 3 ... setting up to insert the input

= 2(2x + 3) + 3

= 4x + 6 + 3

= 4x + 9

Given f(x) = 2x + 3 and g(x) = βx2 + 5, find (g o g)(x).

(g o g)(x) = g(g(x))

= β( )2 + 5 ... setting up to insert the input

= β(βx2 + 5)2 + 5

= β(x4 β 10x2 + 25) + 5

= βx4 + 10x2 β 25 + 5

= βx4 + 10x2 β 20