some help with composition of functions

[speed4baseball]

f(x) = 3/x-7 , g(x)= x^2+5x find f(x) + g(x), f(x)- g(x), f(x) * g(x) , f/g(x)
^any help please? *greatly appreciated

 

[Mrspi]

f(x) = 3/x-7 , g(x)= x^2+5x find f(x) + g(x), f(x)- g(x), f(x) * g(x) , f/g(x)
^any help please? *greatly appreciated

To get you started.....

You want f(x) + g(x)

You KNOW that f(x) = 3/(x - 7) and that g(x) = x[sup:1azpf662]2[/sup:1azpf662] + 5x
So,
f(x) + g(x) = [3 / (x - 7)] + x[sup:1azpf662]2[/sup:1azpf662] + 5x

Simplify the expression on the right-hand side.

The others, finding f(x) - g(x), f(x)*g(x), and f(x)/g(x) will be handled in a similar fashion.

 

[speed4baseball]

how do i simplify 3/x-7 (+) x^2+5x ?

 

[mmm4444bot]

how do i simplify 3/x-7 (+) x^2+5x

Type the grouping symbols around the denominator, instead of around the addition sign.

x^2 + 5x + 3/(x - 7)

Are you supposed to "simplify" this ?

In this form, it represents the quotient (x^2 + 5x) plus the remainder (3) over the divisor (x - 7) that result from dividing some cubic polynomial by x - 7.

If you want to express your result as a single algebraic ratio (i.e., a cubic polynomial divided by x - 7), then you'll need to multiply the quotient (x^2 + 5x) by (x - 7)/(x - 7), in order to get a common denominator. Then, combine the two ratios, and simplify the numerator to get the cubic polynomial.

I think that your answer f(x) + g(x) = x^2 + 5x + 3/(x - 7) is okay just as it is, unless you were given specific instructions for some other final form.