MATH 114 Midterm EXAM with complete
solutions 2024/2025
Domain - ANSWER-The domain is the set of all possible x-values which will make
the function "work", and will output real y-values.
1. Cant divide by zero
2. Cant take an even root of a negative #
ex: root -16 does not exist
but 3 root -8 does exist
3. ln(f(x))---f(x)>0
logbf(x)---f(x)>0
- ANSWER-
To find the inverse of a function - ANSWER-1. solve for x
2. interchange x and y
3. rewrite as f to the -1
Point slope - ANSWER-y-y1=m(x-x1)
Exponent Rules - ANSWER-1/x^n=x^-n
b root x^a=x^a/b
sin^3x=(sinx)^3
sinx^3=sin(x*x*x)
Derivative Rules - ANSWER-f(x)=constant
f^1(x)=0
Derivative rules - ANSWER-f(x)=kx^n
f^1(x)=k(n)x^n-1
Derivative Rules adding - ANSWER-(f(x)+g(x))=f^1(x)+g^1(x)
solutions 2024/2025
Domain - ANSWER-The domain is the set of all possible x-values which will make
the function "work", and will output real y-values.
1. Cant divide by zero
2. Cant take an even root of a negative #
ex: root -16 does not exist
but 3 root -8 does exist
3. ln(f(x))---f(x)>0
logbf(x)---f(x)>0
- ANSWER-
To find the inverse of a function - ANSWER-1. solve for x
2. interchange x and y
3. rewrite as f to the -1
Point slope - ANSWER-y-y1=m(x-x1)
Exponent Rules - ANSWER-1/x^n=x^-n
b root x^a=x^a/b
sin^3x=(sinx)^3
sinx^3=sin(x*x*x)
Derivative Rules - ANSWER-f(x)=constant
f^1(x)=0
Derivative rules - ANSWER-f(x)=kx^n
f^1(x)=k(n)x^n-1
Derivative Rules adding - ANSWER-(f(x)+g(x))=f^1(x)+g^1(x)
