Given that g(x)= 2x+1/5 and f(x)=x+4
Calculate the value of g(-2)
2(-2)+1/5= -3/5
Is this right??
How do i write an expression for gf(x) in the simpliest form??
And how do i find inverse functions such as g`1(x)?
No. -4+1/5= -3 4/5=-3.8 or -19/5
Unless g(x)=(2x+1)/5 which in case then you would be right.
I noticed that Marth already gave you an answer correctly following the order of operation the way you typed it.
You followed the same order in finding g(-2) but made an arithmetic error.
g(-2) = 2(-2) + 1/5
= -4 + 1/5
= -19/5
Perhaps you meant
g(x) = (2x+1)/5
If so, follow Marth's steps using the corrected function for both g(f(x)) and the inverse of g(x)
To calculate the value of g(-2), you substitute -2 into the equation for g(x). So, plugging in -2 into the equation g(x) = 2x + 1/5, you get:
g(-2) = 2(-2) + 1/5
= -4 + 1/5
To simplify this further, you need to find a common denominator for -4 and 1/5, which is 5. So:
g(-2) = (-4 * 5)/5 + 1/5
= -20/5 + 1/5
= -19/5
Therefore, the value of g(-2) is -19/5.
To write an expression for gf(x) in the simplest form, you need to substitute the expression for g(x) into the equation for f(x). So:
gf(x) = f(g(x))
Since g(x) = 2x + 1/5 and f(x) = x + 4, substitute g(x) into f(x):
gf(x) = f(2x + 1/5)
Now simplify the expression if possible, but it cannot be further simplified in this case.
To find the inverse function of g(x), denoted as g^(-1)(x), you need to follow the steps below:
1. Replace g(x) with y, so the equation becomes y = 2x + 1/5.
2. Swap x and y to obtain x = 2y + 1/5.
3. Solve this equation for y. Subtract 1/5 from both sides: x - 1/5 = 2y.
4. Divide both sides by 2 to isolate y: (x - 1/5)/2 = y.
5. Replace y with g^(-1)(x), so the final expression becomes g^(-1)(x) = (x - 1/5)/2.
This is the inverse function of g(x).