# Thread: How to solve f(x) equations

1. ## 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

2. ## Re: How to solve f(x) equations

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
...

3. ## 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?

4. ## Re: How to solve f(x) equations

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?)

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

6. ## 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

7. ## Re: How to solve f(x) equations

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? ...

8. ## Re: How to solve f(x) equations

b)(g+k)(1)=g(1)+k(1)
=-1+(-6)=-7

Hope I am right?

Correct!

10. ## Re: How to solve f(x) equations

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

11. ## Re: How to solve f(x) equations

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

12. ## Re: How to solve f(x) equations

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

f(2)=3
k(2)=6

14. ## Re: How to solve f(x) equations

Originally Posted by KayPee
for part d)I got f(-1)=2-5=-3
Correct!

EDIT: c) is also correct.

15. ## Re: How to solve f(x) equations

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?

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