precalculus check immediately

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suppoe f is a function with domain [1,3]and range[2,5]?
define functions g and h by g(x)=3f(x)and h(x)=f(4x)
what is domain and range of g
what is domain and range of h
I solved it and got it like this
domainof g=[1,3]and range of g=[3,9]
Domain of h=[4,12] and range of h=[2,5]
Is it correct

• precalculus check immediately -

domain of f is also the domain of g and h, since they are defined as multiples of f.

since range of f = [2,5],
range of g = [3*2,3*5] = [6,15]
range of h is [4*2,4*5] = [8,20]

range of g is 3*range of f, not 3*domain of f

domain is the same for all, since g and h are defined for exactly the same values as f is.

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