If #f(x)=x^2# and #g(x)=-12x+7#, how do you find the domain and range of f(x), g(x), and f(g(x))?

1 Answer
MoominDave
Jun 1, 2018

Consider the function input values that work or don't work, and consider the possible function output values from all input values. Specific answers given below.

Explanation:

We'll assume we're working with real numbers here i.e. not complex numbers. Ignore that sentence if you don't know what it means; it's not important to your purposes.

#f(x)=x^2# can be applied to any #x#, so its domain is #[-oo,oo]#. Its output is always positive - because squaring turns a number from negative to positive. So its range is #[0,oo]#.

#g(x)=-12x+7# is simpler. It takes all values, and it returns values not limited to any particular range. Both its domain and range are #[-oo,oo]#.

Happily the range of #g# matches the domain of #f#, and so the domain of #f(g(x))# is equal to the domain of #g(x)#,#[-oo,oo]# while its range is equal to the range of #f(x)#, #[0,oo]#.

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