Question #13537

1 Answer
May 3, 2017

a) g(5x+2)=75x2+35x+4
b) f(x)h(5)=2x125
c) f(x)[h(x)g(x)]=2x411x3+23x224x+10

Explanation:

Given:

f(x)=2x5
g(x)=3x25x+2
h(x)=x3x

a) In order to find g(5x+2) we must plug in for every value of x in g(x) the value (5x+2).

g(x)=3x25x+2
g(5x+2)=3(5x+2)25(5x+2)+2

Now we simplify the expression on the right hand side.

=3(5x+2)(5x+2)5(5x+2)+2

We FOIL (5x+2)(5x+2) and distribute (5) to (5x+2)

=3[(5x)(5x)+(5x)(+2)+(2)(5x)+(+2)(+2)]25x10+2

=3[25x2+10x+10x)+4]25x8

=75x2+60x+1225x8

g(5x+2)=75x2+35x+4

b) For this part, we again substitute the given value of 5 into h(x)

f(x)=2x5
h(x)=x3x

f(x)h(5)=2x5[(5)3(5)]

=2x5125+5

f(x)h(5)=2x125

c) For this part, we need only to perform arithmetic on the given functions:

f(x)=2x5
g(x)=3x25x+2
h(x)=x3x

f(x)[h(x)g(x)]=(2x5)[x3x(3x25x+2)]

Simplifying the expression in the brackets, we get
=(2x5)[x3x3x2+5x2]
=(2x5)[x33x2+4x2]

Now we need to expand and multiply (2x5) by [x33x2+4x2]

=(2x5)[x33x2+4x2]

We can distribute the terms in (2x5) and multiply each of them by [x33x2+4x2]

=(2x)[x33x2+4x2]+(5)[x33x2+4x2]

This gives:

=2x46x3+8x24x
5x3+15x220x+10

Combining like terms, gives:

=2x4+(65)x3+(8+15)x2+(420)x+10

f(x)[h(x)g(x)]=2x411x3+23x224x+10