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Suppose f is a function that takes a real number x and performs the following steps in the order given:
(1) add 1
(2) take the square root
(3) subtract 4
(4) divide into 7
Find an expression for f(x).
f(x) =
X
State the domain of f using interval notation.

Sagot :

Answer:

Expression for f(x) = [tex]\frac{\sqrt{x + 1} - 4}{7}[/tex]

Domain in interval notation: [tex]\:[-1,\:\infty \:)[/tex]

Step-by-step explanation:

[tex]\textrm{Let }f(x)\text{ represent the function}[/tex]

Step 1: Add 1 to [tex]x[/tex]  ==>   x + 1

Step 2: Take square root ==> [tex]\sqrt{x+1}[/tex]

Step 3: Subtract 4: ==>  [tex]\sqrt{x+1} - 4[/tex]

Step 4: Divide by 7 ==> [tex]\frac{\sqrt{x+1} - 4}{7}[/tex]

The expression for f(x) is [tex]\frac{\sqrt{x+1} - 4}{7}[/tex]

The domain of a function is the set of all inputs  for which the function is real and defined

[tex]\sqrt{x+1}[/tex] is real only for positive values of the square root

This means

[tex]\sqrt{x+1} \ge 0[/tex]

Squaring both sides we get

[tex]x + 1 \ge 0[/tex]

Subtracting 1 from both sides we get

[tex]x \ge -1[/tex]

This is the lower limit for [tex]x.[/tex] There is no upper limit

The domain of[tex]f(x)[/tex] is therefore

[tex]x \ge -1[/tex]

In interval notation it is expressed as

[tex][-1,\infty)[/tex]

Note the square bracket on the left and parenthesis on the right. This notation means that -1 is part of the domain but [tex]\infty[/tex]  is not included since at [tex]\infty[/tex]  the function is not defined