i wanna KNOW IF im DOING RIGHT.
Evaluate the difference quotient for the given function. Simplify your answer.
f(x)=x+3/x+1, [f(x)-f(1)]/(x-1)
simplify my answer:
[(x+3)/(x+1) - (1+3)/(1+1)]/(x-1)
= [x+3/x+1 - 4/2] / (x-1)
= [2(x+3)-4(x+1)/2(x+1)] / (x-1)
= [2x+6-4x-4/2(x+1)] / (x-1)
= [-2x+2x/2(x+1)] /(x-1)
= [-2(x-1)/2(x+1)]/(x-1)
so my answer is -1
i mean my answer is -1/(x+1)
correct,
but why didn't you reduce the 4/2 in the second step to 2, it would have made the algebra a lot easier.
oh 4/2 is 2. ok
thanks
To evaluate the difference quotient for the function, we follow these steps:
1. Substitute x into the function and calculate f(x):
f(x) = x+3 / x+1
2. Substitute 1 into the function and calculate f(1):
f(1) = 1+3 / 1+1 = 4/2 = 2
3. Plug the values into the difference quotient formula:
[f(x) - f(1)] / (x-1)
4. Simplify the numerator:
f(x) - f(1) = (x+3 / x+1) - 2 = (x+3 / x+1) - (2(x+1) / x+1)
= (x+3 - 2x - 2) / x+1 = (-x+1) / x+1
5. Simplify the whole expression:
[-x+1 / x+1] / (x-1)
6. Divide the fraction:
-x+1 / x+1 ÷ (x-1) = -x+1 / (x+1)(x-1)
So the simplified answer for the difference quotient is (-x+1) / (x+1)(x-1).