# How to solve f(x) equations

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• Aug 6th 2011, 07:34 AM
KayPee
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
• Aug 6th 2011, 07:41 AM
abhishekkgp
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

...
• Aug 6th 2011, 08:07 AM
KayPee
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?
• Aug 6th 2011, 08:44 AM
abhishekkgp
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?)
• Aug 6th 2011, 11:14 AM
Siron
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:
$\displaystyle \frac{[2(x+h)^2-5]-[2x^2-5]}{h}=\frac{2x^2+4xh+2h^2-5-2x^2+5}{h}=...$
• Aug 6th 2011, 01:54 PM
KayPee
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
• Aug 6th 2011, 01:56 PM
Siron
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? ...
• Aug 6th 2011, 01:58 PM
KayPee
Re: How to solve f(x) equations
b)(g+k)(1)=g(1)+k(1)
=-1+(-6)=-7

Hope I am right?
• Aug 6th 2011, 01:59 PM
Siron
Re: How to solve f(x) equations
Correct!
• Aug 6th 2011, 02:01 PM
KayPee
Re: How to solve f(x) equations
Any clues as to how I should approach parts (c) and (e) ?
• Aug 6th 2011, 02:04 PM
Siron
Re: How to solve f(x) equations
Use:
$\displaystyle (fk)(2)=f(2)\cdot k(2)$
• Aug 6th 2011, 02:11 PM
KayPee
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
• Aug 6th 2011, 02:16 PM
KayPee
Re: How to solve f(x) equations
f(2)=3
k(2)=6

• Aug 6th 2011, 02:17 PM
Siron
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.
• Aug 6th 2011, 02:29 PM
KayPee
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?
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