Question

What is (f+g)(x)? {f(x) = 3x^5+6x^2-5 g(x)=3x^5-5x^4+3x^2-15

Answer 1

Step-by-step explanation

The expression

`(f-g)(x)`

is just another way of writing

`f(x)-g(x)`

Now,

`f(x)=3x^5+6x^2-5`
`g\mleft(x\mright)=3x^5-5x^4+3x^2-15`

Therefore,

`f(x)-g(x)=3x^5+6x^2-5-\lbrack3x^5-5x^4+3x^2-15\rbrack`

expanding the expression in the brackets ( which involves expanding the negative sign) gives

`f(x)-g(x)=3x^5+6x^2-5-3x^5+5x^4-3x^2+15\rbrack`

combining the like terms gives

`f(x)-g(x)=(3x^5-3x^5)+(6x^2-3x^2)+(-5+15)+5x^4`
`=3x^2+10+5x^4`

Hence,

`\boxed{f\mleft(x\mright)-g\mleft(x\mright)=5x^4+3x^2+10.}`

which is our answer!