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Popular >

range of f(x)=1-(x-4)^2

Solution

range

f (x) = 1 - (x - 4)^{2}

Solution

f (x) \leq 1

+1

Interval Notation

(- \infty, 1]

Solution steps

Vertex of

1 - (x - 4)^{2} :

Maximum

(4, 1)

For a parabola

a x^{2} + b x + c

with Vertex

(x_{v}, y_{v})

If

a < 0

the range is

f (x) \leq y_{v}

If

a > 0

the range is

f (x) \geq y_{v}

a = - 1,

Vertex

(x_{v}, y_{v}) = (4, 1)

f (x) \leq 1

Popular Examples

domain of 4/x+6 domain

\frac{4}{x} + 6

domain of f(x)= 5/(x^2-4)domain

f (x) = \frac{5}{x ^{2} - 4}

inverse of f(x)=8x+6 inverse

f (x) = 8 x + 6

line m=0,(0,1)line

m = 0, (0, 1)

domain of f(x)=(x^2-x)/(x^2-1)domain

f (x) = \frac{x ^{2} - x}{x ^{2} - 1}

Frequently Asked Questions (FAQ)

What is the range of f(x)=1-(x-4)^2 ?
The range of f(x)=1-(x-4)^2 is f(x)<= 1