For f(x) = 3x + 4 and g(x) = x - 1. Calculate (f o g)(x).
For f(x) = 3x + 2 and g(x) = x². Calculate (f o g)(-2).
Consider the function. f(x)= -2x+1. Find the inverse of f(x).
Please help! How do I solve this?
f of g= 3(x-1)+4=3x+1
f of g = 3(-2^2)+2=14
f(x)=-2z+1
y=-2x+1
2x=-y+1
x= -y/2+1/2
finverse= -x/2+1/2
Can you somewhat explain how you got 1 and 2,Im trying to understand D:
wouldn't that be -10?
(f o g)(x) is defined as f(g(x))
so
f(g(x)) = f(x-1) , remember f(x) = 3x+4
f(g(x)) = 3(x-1) + 4 = 3x + 1 , same as bob
or f(g(x))
= 3g(x) + 4
= 3(x-1) + 4 = 3x + 1 , like bob had
in #2
(f o g)(-2)
= f(g(-2)) ----> g(-2) = (-2)^2 = 4
= f(4)
= 3(4) + 2 = 14
last one:
Here is how I do these:
y = -2x + 1
step#1: interchange the x and y variables
x = -2y + 1
step#2: solve this new equation for y
2y = -x + 1
y = (-1/2)x + 1/2 or as bob had it: y = -x/2 + 1/2
To calculate (f o g)(x), you need to substitute g(x) as the input into f(x) and simplify the expression.
For the first question,
f(x) = 3x + 4 and g(x) = x - 1. To find (f o g)(x), substitute g(x) into f(x) as follows:
(f o g)(x) = f(g(x)) = f(x - 1)
Now, replace x from f(x) with (x - 1):
(f o g)(x) = 3(x - 1) + 4
Simplify the expression:
(f o g)(x) = 3x - 3 + 4
(f o g)(x) = 3x + 1
So, (f o g)(x) = 3x + 1.
For the second question,
f(x) = 3x + 2 and g(x) = x². To find (f o g)(-2), substitute -2 into g(x) as follows:
(f o g)(-2) = f(g(-2)) = f((-2)²)
Evaluate (-2)² first:
(-2)² = 4
Now, replace x from f(x) with 4:
(f o g)(-2) = 3(4) + 2
Simplify the expression:
(f o g)(-2) = 12 + 2
(f o g)(-2) = 14
Therefore, (f o g)(-2) = 14.
To find the inverse of a function, f(x) = -2x + 1, follow these steps:
1. Replace f(x) with y:
y = -2x + 1.
2. Swap the x and y variables:
x = -2y + 1.
3. Solve the equation for y:
x - 1 = -2y.
Divide both sides by -2 to isolate y:
y = (x - 1) / -2.
4. Replace y with f^(-1)(x):
f^(-1)(x) = (x - 1) / -2.
So, the inverse of f(x) = -2x + 1 is f^(-1)(x) = (x - 1) / -2.