Let f(x) = 8x3 + 18x2 − 10 and g(x) = 4x + 1. Find f of x over g of x.

Find f of x over g of x.

=512x³+672²+210x+16

Step-by-step explanation:

Step one

Given

f(x) = 8x³ + 18x² − 10 and

g(x) = 4x + 1

Find f(g(x))

Substituting 4x + 1 for x in f(x)

We have

f(g(x)) =8(4x+1)³+18(4x+1)²-10

=8(4x+1)(4x+1)(4x+1)+18(4x+1)(4x+1)-10

Opening the brackets

=8(4x+1)(16x²+8x+1)+18(16x²+8x+1)-10

=(32x+8)(16x²+8x+1)+288x²+144x+18-10

512x³+256x²+32x+128x²+64x+8+288x²+144x+18-10

Collecting like terms we have

512x³+256x²+128x²+288x²+32x+64x+144x +8+18-10

=512x³+672²+210x+16

8/k

step-by-step explanation:

let x and 400 - x be the two numbers.  

==> 0.80x + 0.85(400 - x) = 400 - 68 from the statement of the problem.  

< ==> 0.80x + 0.85(400 - x) = 400 - 68  

==> 340 - 0.05x = 332  

< ==> -0.05x = -8 ==> x = 160, the first number ==> 400 - x = 240, the second number.