tentukan invers fungsi dibawah ini= a) f(x)= 3x^2+4/2x^2-5 b) f(x)=(1-x^3)^1/5 c)f(x)=2x+5/x-1
Matematika
lutfebri
Pertanyaan
tentukan invers fungsi dibawah ini=
a) f(x)= 3x^2+4/2x^2-5
b) f(x)=(1-x^3)^1/5
c)f(x)=2x+5/x-1
a) f(x)= 3x^2+4/2x^2-5
b) f(x)=(1-x^3)^1/5
c)f(x)=2x+5/x-1
1 Jawaban
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1. Jawaban EdiHeaven
a) f(x)= 3x^2+4/2x^2-5
y = 3x^2+4/2x^2-5
y(2x²-5)=3x²+4
2x²y - 5y = 3x²+4
2x²y-3x²= 5y+4
x²(2y-3)=5y+4
x²=5y + 4 / 2y-3
x = √( 5y + 4 / 2y-3)
f-¹(x) = √(5x+4 / 2x-3)
b) f(x)=(1-x^3)^1/5
y= (1-x^3)^1/5
y^5 = 1-x³
x³= 1-y^5
x = (1-y^5)^1⅓
f-¹(x) = (1-x^5)^⅓
c)f(x)=2x+5/x-1
y = 2x+5/x-1
y(x-1)=2x+5
xy-y=2x+5
xy-2x=y+5
x(y-2)=y+5
f-¹(x) = x+5 / x-2