Given h(x) = sqrt(2 - x), find the domain and range for h(x) and h^-1(x)...(the inverse) using interval notation, and explain how you found the domain and range of [the inverse] of h(x)...
Range of h(x)...
Domain of h^-1(x)...why?
Range of h^-1(x)...why?
2006-11-02 04:13:38 · 1 answers · asked by puffer fish 5 in Education & Reference ➔ Homework Help
The domain of a function is those x-values for which it is defined, while the range is those y-values that are actually answers of the function.
The range of any square root function is [0,oo) (numbers greater than or equal to zero) because without a negative sign, the indicated square root is positive.
The inverse of this function can be found by switching around the variables "x" and "y". It would be:
x = SQR(2 - y)
x^2 = 2 - y
x^2 - 2 = -y
-x^2 + 2 = y = h^-1(x)
This function is defined for all real numbers, so its domain should be (-oo,oo).
The maximum y-value of this function is 2, and it can have any value less than that, so the range would be (-oo,2].
2006-11-04 00:06:40 · answer #1 · answered by dmb 5 · 0⤊ 0⤋