1. ## functions

am having some problems with these equations

given tha f and g are functions where the target set and source sets are the set of real numbers and

f(x) = 10-3x
g(x) = 2
1+3

calculate

i) f(2)
ii)g(-3)
iii) fog(2)

write down an expression giving
iv) g o f (x)
v)f-1(x)

again thanks for any help

2. Originally Posted by red55
am having some problems with these equations

given tha f and g are functions where the target set and source sets are the set of real numbers and

f(x) = 10-3x
g(x) = 2/1+3
Sure you've typed g correctly?

3. Originally Posted by red55
am having some problems with these equations

given tha f and g are functions where the target set and source sets are the set of real numbers and

f(x) = 10-3x
g(x) = 2
1+3

calculate

i) f(2)
ii)g(-3)
iii) fog(2)

write down an expression giving
iv) g o f (x)
v)f-1(x)

again thanks for any help
i) f(2) where 2 is your x value... this is the function f(x) evaluated at 2 so you plug in 2 where ever you have an x in your function

f(2) = 10-3(2) = 4

ii) Unforutnately your g function is not reasonable, I think there is an error...

but g(-3) would be done the same way, substitute x with -3 because you are evaluating the function g(x) at -3

iii) the composite is not as scary as it seems...(well depending on your functions anyway...)
f(g(x)) means that the functions f(x) is evaluated at g(x) so substitute x in f(x) with g(x)...

you will have

f(g(x)) = 10 - 3(g(x))

iv) g compositite f is the same as iii), but instead you use f(x) as your x-value and plug into all x's in g(x)

v) f-1 is f inverse.

f(x) = 10 - 3x Solve for x

f(x)= 10 - 3x ---> move the 3x to the left side of the = sign and the f(x) to the right of the = sign

10 - f(x) = 3x ----> get x by itself by dividing both sides by 3

(10 - f(x))/3 = x -----> no that you have this just swap x with f(x)

(10 - x)/3 = f(x) ------> this is your inverse function

I hope that helps

4. Originally Posted by red55
am having some problems with these equations

given tha f and g are functions where the target set and source sets are the set of real numbers and

f(x) = 10-3x
g(x) = 2
1+3

calculate

i) f(2)
ii)g(-3)
iii) fog(2)

write down an expression giving
iv) g o f (x)
v)f-1(x)

again thanks for any help
Hello,

I assume that the function g reads:
$g(x) = \frac{2}{x+3}$

If so you'll get at:

ii) $g(-3) \notin \mathbb{R}$ because you have to divide by zero.

iii) $f \circ g(2)=10 - 3 \cdot \left( \frac{2}{2+3} \right) = 10 -\frac{6}{5} = \frac{44}{5}$

iv) $g \circ f(x) = g(f(x))=\frac{2}{10 - 3x +3} = \frac{2}{13-3x}$