Diketahui f(x) = x² - 2. Hitunglah:
a. f(x² + 1) ...

Question

Diketahui f(x) = x² - 2. Hitunglah: 
a. f(x² + 1) + f(x²) - f(1)

Wastu N · Accepted Answer

Jawab:
f (x) = x² - 2

f (x² + 1) + f (x²) - f (1)
= (x² + 1) (x² + 1) - 2 + (x²)² - 2 - |(1² - 2)|
= x⁴+ 2x² + 1 - 2 + - 2 + 1
=x⁴+x⁴ + 2x² + 1 - 2 - 2 + 1
= 2x⁴+ 2x² - 2

Muhammad A · Accepted Answer

substitusi X=X²+1
>f(x)=X²-2
>f(x²+1)=(X²+1)²-2
>f(x²+1)=X⁴+2X²+1-2
>f(X²+1)=X⁴+2X²-1

substitusi X=X²
>f(x)=X²-2
>f(x²)=(x²)²-2
>f(X²)=X⁴-2

substitusi X=1

>f(x)=X²-2
>f(1)=1-2=-1

•f(X²+1)+f(X²)-f(1)
•(x⁴+2X²-1)+(X⁴-2)-(-1)
•2X⁴+2X²-1-2+1
•2X⁴+2X²-2
•2(X⁴+X²-1)

jadi jawabannya adalah. 2(X⁴+X²-1)

Diketahui f(x) = x² - 2. Hitunglah: a. f(x² + 1) + f(x²) - f(1)