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kodGreya [7K]
3 years ago
12

If f(x) = 2x and g(x) = sqrt x,what is the domain of (fog)(x)?

Mathematics
1 answer:
Norma-Jean [14]3 years ago
7 0

Answer:

All Real x larger or equal zero

or in inequality form: x\geq 0

or in interval notation: [0,\infty)

Step-by-step explanation:

If f(x)=2x and g(x)=\sqrt{x}, then using the definition for the composition of functions (fo\,g)(x)=f(g(x)), we get:

(fo\,g)(x)=f(g(x)) \\(fo\,g)(x)=f(\sqrt{x} )\\(fo\,g)(x)=2\,\sqrt{x}

Base on this final expression, we understand that the Domain (numbers that can be used as input of the function and produce a real number as result) of this new function is limited to those x-values larger than or equal to zero. Negative numbers inside the square root will not produce a real number.

Therefore, the Domain is restricted to All Real numbers larger than or equal to o (zero).

This statement can also be given in inequality form as x\geq 0

or in interval notation: [0,\infty)

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