Pertanyaan

Jika f ( x ) = x + 1 , g ( x ) = x 2 , dan h ( x ) = x − 2 x , maka ( h ∘ f ∘ g ) = ....

Jika $f (x) = x + 1$ , $g (x) = x^{2}$ , dan $h (x) = \frac{x}{x - 2}$ , maka $(h \circ f \circ g) = ....$

Y. Umi

Master Teacher

Mahasiswa/Alumni Universitas Gadjah Mada

Jawaban terverifikasi

Jawaban

.

open parentheses h ring operator f ring operator g close parentheses open parentheses x close parentheses equals

$fraction numerator italic x squared plus 1 over denominator italic x squared minus sign 1 end fraction$ .

Pembahasan

Jika , , dan , maka Jadi, .

Jika f open parentheses x close parentheses equals x plus 1 , g open parentheses x close parentheses equals x squared , dan $h open parentheses x close parentheses equals fraction numerator x over denominator x minus 2 end fraction$ , maka

$table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses h ring operator f ring operator g close parentheses open parentheses x close parentheses end cell equals cell h open parentheses f open parentheses g open parentheses x close parentheses close parentheses close parentheses end cell row blank equals cell h open parentheses f open parentheses x squared close parentheses close parentheses end cell row blank equals cell h open parentheses x squared plus 1 close parentheses end cell row blank equals cell fraction numerator x squared plus 1 over denominator x squared plus 1 minus 2 end fraction end cell row blank equals cell fraction numerator x squared plus 1 over denominator x squared minus 1 end fraction end cell end table$

Jadi, open parentheses h ring operator f ring operator g close parentheses open parentheses x close parentheses equals $fraction numerator italic x squared plus 1 over denominator italic x squared minus sign 1 end fraction$ .

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