Consider (f(x)=x^ 2 -3x+a ) ( (a R )) and (g(x)= x )

MATHEMATICS · Single correct · A Level · Mathematics · Algebra and Functions · Algebra and Functions

Problem

Consider

f(x)=x^{2}-3x+a

(

a\in\mathbb R

) and

g(x)=\sqrt{x}

. For which values of

a

does the composite function

g\circ f

have domain equal to

\mathbb R

? (a)

a=\dfrac{9}{4}

only (b)

a\ge\dfrac{9}{4}

(c)

a\le\dfrac{9}{4}

(d)

a\ge 0

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