What is the domain and range for #f(x)=sqrt(x-1)#?

1 Answer
May 10, 2018

Answer:

#" "#
#color(blue)("Domain: " x>=1#, Interval Notation: #color(brown)([1, oo)#

#color(blue)("Range: " f(x)>=0#, Interval Notation: #color(brown)([0, oo)#

Explanation:

#" "#
#color(green)"Step 1:"#

Domain:

The domain of the given function #f(x)# is the set of input values for which #f(x)# is real and defined.

Point to note:

#color(red)(sqrt(f(x)) = f(x)>=0#

Solve for #(x-1)>=0# to obtain #x>=1#.

Hence,

#color(blue)("Domain: " x>=1#

Interval Notation: #color(brown)([1, oo)#

#color(green)"Step 2:"#

Range:

Range is the set of values of the dependent variable used in the function #f(x)# for which #f(x)# is defined.

Hence,

#color(blue)("Range: " f(x)>=0#

Interval Notation: #color(brown)([0, oo)#

#color(green)"Step 3:"#

Additional note:

The function #y = f(x)= sqrt(x-1)# has no asymptotes.

Create a data table using values for #x# and corresponding values for #y#:

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Observe that #Zero# and #"Negative values"# of #x# make the function #f(x)# #"undefined"# at those points.

Graph #f(x) = sqrt(x-1# to verify the results obtained:

enter image source here