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.
Take your function,
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