How to solve f(x) equations

Hi How do I approach the question below:

Let f(x)= 2x^2 - 5,g(x)= 3-4x, k(x) = 6x/(x^2-2)

Find the following and simplify:

a)g(-1)

b) (g+k)(1)

c)(fk)(2)

d f(g(1)

e (f(x+h) - f(x))/h

I am extremely rusty.Can anyone help me solve these.Give me leads

For instance for a)g(-1)

Do I substitute 1 into the equation: g(x)= 3-4x

Thanks

Re: How to solve f(x) equations

Quote:

Originally Posted by

**KayPee** Hi How do I approach the question below:

Let f(x)= 2x^2 - 5,g(x)= 3-4x, k(x) = 6x/(x^2-2)

Find the following and simplify:

a)g(-1)

b) (g+k)(1)

c)(fk)(2)

d f(g(1)

e (f(x+h) - f(x))/h

I am extremely rusty.Can anyone help me solve these.Give me leads

For instance for a)g(-1)

Do I substitute 1 into the equation: g(x)= 3-4x

No, you have to substitute -1 in the equation g(x)=3-4x. so g(-1)=3-4*(-1)=7.

Thanks

...

Re: How to solve f(x) equations

So b) (g+k)(1)

I have to add 7 to 6x/(x^2-2) and multiply by 1?

Re: How to solve f(x) equations

Quote:

Originally Posted by

**KayPee** So b) (g+k)(1)

I have to add 7 to 6x/(x^2-2) and multiply by 1?

(g+k)(1)=g(1)+k(1). g(1) is not 7. g(1)=-1. (why?)

Re: How to solve f(x) equations

d) If you have to simplify:

$\displaystyle f[g(1)]$, calculate $\displaystyle g(1)=3-4.1=-1$ and now you'll get: $\displaystyle f(-1)=...$?

e) If you have to simplify:

$\displaystyle \frac{f(x+h)-f(x)}{h}$ and you know: $\displaystyle f(x)=2x^2-5$, then substitute the given into the equation:

$\displaystyle \frac{[2(x+h)^2-5]-[2x^2-5]}{h}=\frac{2x^2+4xh+2h^2-5-2x^2+5}{h}=...$

Re: How to solve f(x) equations

I got it g(x)=3-4x

g(1)=3-4

=-1

in that same vein

k(1)=6/-1=-6

Re: How to solve f(x) equations

Quote:

Originally Posted by

**KayPee** I got it g(x)=3-4x

g(1)=3-4

=-1

in that same vein

k(1)=6/-1=-6

Right!

Can you solve your exercices now? ...

Re: How to solve f(x) equations

b)(g+k)(1)=g(1)+k(1)

=-1+(-6)=-7

Hope I am right?

Re: How to solve f(x) equations

Re: How to solve f(x) equations

Any clues as to how I should approach parts (c) and (e) ?

Re: How to solve f(x) equations

Use:

$\displaystyle (fk)(2)=f(2)\cdot k(2)$

Re: How to solve f(x) equations

Quote:

Originally Posted by

**Siron** d) If you have to simplify:

$\displaystyle f[g(1)]$, calculate $\displaystyle g(1)=3-4.1=-1$ and now you'll get: $\displaystyle f(-1)=...$?

e) If you have to simplify:

$\displaystyle \frac{f(x+h)-f(x)}{h}$ and you know: $\displaystyle f(x)=2x^2-5$, then substitute the given into the equation:

$\displaystyle \frac{[2(x+h)^2-5]-[2x^2-5]}{h}=\frac{2x^2+4xh+2h^2-5-2x^2+5}{h}=...$

for part d)I got f(-1)=2-5=-3

Re: How to solve f(x) equations

f(2)=3

k(2)=6

answer for (fk)(2)=18 ?

Re: How to solve f(x) equations

Quote:

Originally Posted by

**KayPee** for part d)I got f(-1)=2-5=-3

Correct!

EDIT: c) is also correct.

Re: How to solve f(x) equations

Quote:

Originally Posted by

**KayPee** for part d)I got f(-1)=2-5=-3

I guess for e I cannot arrive at a single figure .It just has to be simplified like you have done right?