+956 If f(x) =1/(logx) and g(x) = 1/(8+x), what is the domain of (fxg)(x)?
a) {x e R | x > 0 and x can't equal -8}
b) {x e R | x > 0 and x can't equal 1}
c) {x e R | x > 0}
d{ {x e R | x can't equal -9 and 1}
+9479 (f × g)(x) = ( 1 / (log x) )( 1 / (8 + x) )
Since log x is part of the function, we have the restriction x > 0
Since log x is in a denominator, we have the restriction log x ≠ 0
log x ≠ 0
x ≠ 100
x ≠ 1
Since 8 + x is in a denominator, we have the restriction 8 + x ≠ 0
8 + x ≠ 0
x ≠ -8 Notice that this is already accounted for with x > 0
So the domain is all real x values such that x > 0 and x ≠ 1
+9479 (f × g)(x) = ( 1 / (log x) )( 1 / (8 + x) )
Since log x is part of the function, we have the restriction x > 0
Since log x is in a denominator, we have the restriction log x ≠ 0
log x ≠ 0
x ≠ 100
x ≠ 1
Since 8 + x is in a denominator, we have the restriction 8 + x ≠ 0
8 + x ≠ 0
x ≠ -8 Notice that this is already accounted for with x > 0
So the domain is all real x values such that x > 0 and x ≠ 1
