Given that f(x)=x^2+2,x<=0 and g(x)= - sqrt(1-2x). Find
1) f[g(x)] and state its domain and range.
2) State if g[f(x)] is defined, giving the reason
Any1 can help plz?
1) f[g(x)] and state its domain and range.
2) State if g[f(x)] is defined, giving the reason
Any1 can help plz?
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Couple of steps.
1). Insert -sqrt(1-2x) in place of the x in f(x): y = (-sqrt(1-2x))^2 + 2
2). -sqrt(1-2x) X -sqrt(1-2x) = sqrt((1-2x)(1-2x)) = (1-2x) : ex :( sqrt(4) x sqrt(4) = sqrt(4 * 4) = 4
3) so f(g(x)) = 1-2x + 2 = f(g(x)) = 3-2x or y = -2x +3 (which is a line)
4) a line is a function so it is defined
5) domain and range all real numbers
1). Insert -sqrt(1-2x) in place of the x in f(x): y = (-sqrt(1-2x))^2 + 2
2). -sqrt(1-2x) X -sqrt(1-2x) = sqrt((1-2x)(1-2x)) = (1-2x) : ex :( sqrt(4) x sqrt(4) = sqrt(4 * 4) = 4
3) so f(g(x)) = 1-2x + 2 = f(g(x)) = 3-2x or y = -2x +3 (which is a line)
4) a line is a function so it is defined
5) domain and range all real numbers