for domain, x is restricted because you can't take the square root of a negative number and get a real answer. So you solve 4x-7=0 to get 7/4 and x cannot be less than 7/4 or you will get a negative number. In notation its [7/4, positive infinity) positive infinity looks like an 8 turned sideways. The bracket in the first part is inclusive because the answer includes 7/4. This is because if x=7/4, it will be √(0), which is just 0.
range is the y --> what this can =
so its [0, positive infinity) because the smallest result you can get here is 0. And you CAN get 0, so it's included.
positive/negative infinity is never inclusive. That's just how it goes.
to find the inverse of f, just switch the x's for y's and the y's for x's. Then solve for y. here, f(x) is your y because it is the output. f(x) is always the y in functions.
Answers & Comments
for domain, x is restricted because you can't take the square root of a negative number and get a real answer. So you solve 4x-7=0 to get 7/4 and x cannot be less than 7/4 or you will get a negative number. In notation its [7/4, positive infinity) positive infinity looks like an 8 turned sideways. The bracket in the first part is inclusive because the answer includes 7/4. This is because if x=7/4, it will be √(0), which is just 0.
range is the y --> what this can =
so its [0, positive infinity) because the smallest result you can get here is 0. And you CAN get 0, so it's included.
positive/negative infinity is never inclusive. That's just how it goes.
to find the inverse of f, just switch the x's for y's and the y's for x's. Then solve for y. here, f(x) is your y because it is the output. f(x) is always the y in functions.
so...
x=√(4y-7) --> x's and y's are all switched.
x²=4y-7 --> square both sides.
x²+7=4y --> add 7.
(x²+7)/4=y --> divide by 4.
f-1(x)=(x²+7)/4 --> write in function notation.
Hope this helps =]
yay math! haha