Question

Find the range of function f(x)=3/2-xsquare

Answer 1

To find the Range write the variable in terms of f(x).
3/2-f(x)=x²
x=√(3/2-f(x))
Since under root term is always ≥0
3/2-f(x)≥0
f(x)≤3/2
So the Domain of f(x) is Range of x.\
Range of x is (-∞,3/2]

Answer 2

Answer:

The range of the function is $(-\infty, \frac{3}{2}]$.

Step-by-step explanation:

The given function is

$f(x)=\frac{3}{2}-x^2$

It can be rewritten as

$f(x)=-x^2+\frac{3}{2}$      .... (1)

Here, leading coefficient is -1<0. So, it is a downward parabola and vertex of a downward parabola is the point of maxima.

The vertex form of a parabola is

$g(x)=a(x-h)^2+k$           .... (2)

where, a is constant (h,k) is vertex of the parabola.

From (1) and (2) we get

$h=0,k=\frac{3}{2}$

It means vertex of the parabola is (0,3/2). It means maximum output value of the given function is 3/2. So, range of the function is

$Range=\{y|y\leq \frac{3}{2},y\in R\}$

$Range=(-\infty, \frac{3}{2}]$

Therefore the range of the function is $(-\infty, \frac{3}{2}]$.