how to find the domain and range of a COMPOSITE function?

Question

anonymous · Answer

attachment

gorv · Answer

welcome to OS :)

amistre64 · Answer

the domain is a working of the original domains and exclusions for the new function

amistre64 · Answer

since 4 is not defined in the domain of F,  then the composite is not defined at x=4 either since F remains undefined

anonymous · Answer

thank you :D but for f(g(x)) the answer is D: [-3.5, 4] R: [0,2] but i don't know how to get it.

amistre64 · Answer

f(g) is the composition;  so wihtout further information the range of g is adapted as the domain of f for all range g in domain f

amistre64 · Answer

f is defined for all x values from -4 to 3,  g outputs are from 0 to 4

so the composition is only defined for all g from 0 to 3 is what im reading

amistre64 · Answer

the range of f is therefore the section of f between 0 and 3,  which gives outputs of 0 to 2

amistre64 · Answer

i see what they did now

amistre64 · Answer

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