What is the domain and range of $y = arccos (\frac{x - 4}{8})$ $y = arccos({x-4}/{8})$ ?

Question

What is the domain and range of $y = arccos (\frac{x - 4}{8})$ $y = arccos({x-4}/{8})$ ?

1 Answer

Related questions

How do you use the properties of inverse trigonometric functions to evaluate $tan (arcsin (0.31))$ $tan(arcsin (0.31))$ ?
What is $sin ({sin}^{- 1} \frac{\sqrt{2}}{2})$ $\sin ( sin^{-1} frac{sqrt{2}}{2})$ ?
How do you find the exact value of $cos ({tan}^{- 1} \sqrt{3})$ $\cos(tan^{-1}sqrt{3})$ ?
How do you evaluate ${sec}^{- 1} \sqrt{2}$ $\sec^{-1} \sqrt{2}$ ?
How do you find $cos ({cot}^{- 1} \sqrt{3})$ $cos( cot^{-1} sqrt{3} )$ without a calculator?
How do you rewrite ${sec}^{2} ({tan}^{- 1} x)$ $sec^2 (tan^{-1} x)$ in terms of x?
How do you use the inverse trigonometric properties to rewrite expressions in terms of x?
How do you calculate ${sin}^{- 1} (0.1)$ $sin^-1(0.1)$ ?
How do you solve the inverse trig function ${cos}^{- 1} (- \frac{\sqrt{2}}{2})$ $cos^-1 (-sqrt2/2)$ ?
How do you solve the inverse trig function $sin ({sin}^{- 1} (\frac{1}{3}))$ $sin(sin^-1 (1/3))$ ?

Impact of this question

1775 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-08-24T05:27:46

Domain $= [- 4, 12]$ $=[-4,12]$ , and,

Range $= [0, π]$ $=[0,pi]$ .

Explanation:

Let us recall the Defn. of $a r c cos$ $arc cos$ function :

$a r c cos t = θ, | t | \leq 1, \Leftrightarrow cos θ = t, θ \in [0, π]$ $arc cost=theta, |t|<=1, iff costheta=t, theta in [0,pi]$

Hence, the Domain for the given function, is, given by,

$∣ ∣ ∣ \frac{x - 4}{8} ∣ ∣ ∣ \leq 1 \Rightarrow | x - 4 | \leq 8 \Rightarrow 4 - 8 \leq x \leq 4 + 8,$ $|(x-4)/8|<=1 rArr |x-4|<=8 rArr 4-8<=x<=4+8,$ i.e.,

$- 4 \leq x \leq 12, or, x \in [- 4, 12]$ $-4<=x<=12, or, x in [-4,12]$

The Range is $y \in [0, π]$ $y in [0,pi]$

Science

Math

Humanities

... and beyond

What is the domain and range of $y = arccos (\frac{x - 4}{8})$ $y = arccos({x-4}/{8})$ ?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

What is the domain and range of y=arccos(x−48)y = arccos({x-4}/{8})?

1 Answer

Explanation:

Related questions

Impact of this question

What is the domain and range of $y = arccos (\frac{x - 4}{8})$ $y = arccos({x-4}/{8})$ ?